Some Convergence Strategies for the Alternating Generalized Projection Method

In this paper we extend the application of the alternating projection algorithm to solve the problem of finding a point in the intersection of n sets (ngeq2), which are not all of them convex sets. Here we term such method as alternating generalized projection (AGP) method. In particular, we are interested in addressing the problem of avoiding the so-called trap points, which may prevent an algorithm to obtain a feasible solution in two or more sets not all convex. Some strategies that allow us to reach the feasible solution are established and conjectured. Finally, we present simple numerical results that illustrate the efficiency of the iterative methods considered.